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A randomised algorithm is proposed for computing globally optimal static-output-feedbacks for large-scale systems. The algorithm is based on the Ray-Shooting Method and involves some heuristics to accelerate the search. We also improve the basic Ray-Shooting Algorithm and make the search in the controller parameter-space (which generally, is much more smaller than the certificate parameter-space), thus enabling its efficient use for large-scale systems. [ABSTRACT FROM AUTHOR]

A randomised optimisation method, called the ray-shooting method that efficiently solves the minimisation problem of continuous functions over compact non-convex unconnected regions, was introduced recently. Based on the ray-shooting method, an algorithm is suggested for solving the problems of structured and structured-sparse stabilising static-output-feedbacks. The algorithm presented here is a randomised algorithm, with a proof of convergence in probability. Its practical implementation has a good performance, in terms of quality of controllers, percent of success and run-time. [ABSTRACT FROM PUBLISHER]

This paper is concerned with theH∞model reduction for negative imaginary (NI) systems. For a given linear time-invariant system that is stable and NI, our goal is to find a stable reduced-order NI system satisfying a pre-specifiedH∞approximation error bound. Sufficient conditions in terms of matrix inequalities are derived for the existence and construction of anH∞reduced-order NI system. Iterative algorithms are provided to solve the matrix inequalities and to minimise theH∞approximation error. Finally, a numerical example is used to demonstrate the effectiveness of the proposed model reduction method. [ABSTRACT FROM PUBLISHER]

The main focus of this article is to present a proposal to solve, viaUDUTfactorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor–critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model. [ABSTRACT FROM AUTHOR]

This paper studies maintenance policies for multi-component systems in which failure interactions and opportunistic maintenance (OM) involve. This maintenance problem can be formulated as a Markov decision process (MDP). However, since an action set and state space in MDP exponentially expand as the number of components increase, traditional approaches are computationally intractable. To deal with curse of dimensionality, we decompose such a multi-component system into mutually influential single-component systems. Each single-component system is formulated as an MDP with the objective of minimising its long-run average maintenance cost. Under some reasonable assumptions, we prove the existence of the optimal (n,N) type policy for a single-component system. An algorithm to obtain the optimal (n,N) type policy is also proposed. Based on the proposed algorithm, we develop an iterative approximation algorithm to obtain an acceptable maintenance policy for a multi-component system. Numerical examples find that failure interactions and OM pose significant effects on a maintenance policy. [ABSTRACT FROM AUTHOR]

In this article, the job shop scheduling problem with two batch-processing machines is considered. The machines have limited capacity and the jobs have non-identical job sizes. The jobs are processed in batches and the total size of each batch cannot exceed the machine capacity. The processing times of a job on the two machines are proportional. We show the problem of minimising makespan is NP-hard in the strong sense. Then we provide an approximation algorithm with worst-case ratio no more than 4, and the running time of the algorithm is O(n log n). Finally, the performance of the proposed algorithm is tested by different levels of instances. Computational results demonstrate the effectiveness of the algorithm for all the instances. [ABSTRACT FROM PUBLISHER]

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach. [ABSTRACT FROM PUBLISHER]

The single-vehicle cyclic inventory routing problem (SV-CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer, selected for replenishments, the supplier collects a corresponding fixed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each and to design the vehicle route so that the resulting profit (difference between the total reward and the total logistical cost) is maximised while preventing stockouts at each of the selected customers. This problem appears often as a sub-problem in many logistical problems. In this article, the SV-CIRP is formulated as a mixed-integer program with a nonlinear objective function. After a thorough analysis of the structure of the problem and its features, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of a savings-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general, the gap may get as large as 25%, which justifies the effort to continue exploring and developing exact and approximation algorithms for the SV-CIRP. [ABSTRACT FROM PUBLISHER]

Manufacturing and transportation costs have increased substantially in recent years as demands for raw materials and fossil-based energy continue to grow. To buffer potential loss and increase order quantity, manufacturers often specify requirements when retailers place orders. One widely applied practice is to set up a minimum order size requirement, which is largely driven to achieve improved economies in the production and transportation processes. Many buyers, on the other hand, are left perplexed as to how to effectively establish their inventory policies. In this article, we study a multi-item model in which a retailer faces a minimum order size requirement from its manufacturer and the demands for these items are stochastic. In particular, the total order size of all items has to be at least the minimum order size whenever the retailer decides to place an order. We construct the exact model and develop an accurate lower bound approximation. To better understand the dynamics of the system and the ordering behaviour, we characterise important properties and based on which we propose effective heuristic strategies of simple structure for the multi-item model. Through extensive numerical studies, we show that the policies are consistently robust under a variety of different parameters. Important insights into the systems are also provided. [ABSTRACT FROM AUTHOR]